I don't know exactly what is necessary with the cards. DirecTV is kind of unsure of their own policy, though they will sometimes state they aren't supposed to, but allow you to swap cards from one unit to another anyway. You still have to get on the phone with them.
If you have an HD display, then you really should look into HD DirecTV for your display. The difference between HD and SD (standard def) TV is tremendous.
You probably will not see an improvement of your image using component cables vs. S-video cables. You will still be looking at SD material which will be using the processor inside the DirecTV box to convert it to component instead of a processor inside your display processing the signal. It is still a SD signal and won't approach the quality you would get with a full-on HD signal.
Tivo is available embedded in HD boxes. Samsung makes an HD/Tivo DirecTV unit that is excellent for HD & SD recordings. The problem is you upgraded your display... now the sources need that upgrade as well.
Good luck.